Data Clustering via Uncorrelated Ridge Regression

Ridge regression is frequently utilized by both supervised and semisupervised learnings. However, the trivial solution might occur, when ridge regression is directly applied for clustering. To address this issue, an uncorrelated constraint is introduced to the ridge regression with embedding the manifold structure. In particular, we choose uncorrelated constraint over orthogonal constraint, since the closed-form solution can be obtained correspondingly. In addition to the proposed uncorrelated ridge regression, a soft pseudo label is utilized with \ell {1} ball constraint for clustering. Moreover, a brand new strategy, i.e., a rescaled technique, is proposed such that optimal scaling within the uncorrelated constraint can be achieved automatically to avoid the inconvenience of tuning it manually. Equipped with the rescaled uncorrelated ridge regression with the soft label, a novel clustering method can be developed based on solving the related clustering model. Consequently, extensive experiments are provided to illustrate the effectiveness of the proposed method.